Stability of a σP-unital continuous field algebra

We study the question of whether stability is preserved under the operation of forming a continuous field algebra. This is not necessarily true when the base space is infinite-dimensional. However, it is always true when the base space is an n-cube or an n-torus, and when the continuous field algebra is σP-unital. Specifically, we prove the following.Theorem 0.1 – Let A be a σP-unital separable maximal full algebra of operator fields with base space either an n-cube X=n[0,1] or an n-torus X=Tn and fibre algebras {Ax}x∈X. If Ax is stable for all x∈X then A is a stable C∗-algebra.We also show that, under the same hypotheses, the corona factorization property is also preserved under the formation of continuous field algebras.Theorem 0.2 – Let A be a σP-unital separable maximal full algebra of operator fields with base space either an n-cube X=n[0,1] or an n-torus X=Tn and fibre algebras {Ax}x∈X. If Ax has the corona factorization property for all x∈X then A also has the corona factorization property.